Statistical mechanics of cross-bridge action are considered in order to develop constitutive equations that express fiber tension as a function of degree of activation and time history of speed contraction. The kinetic equation of A.F. Huxley is generalized to apply to the partially activated state. The rate parameters of attachment and detachment and cross-bridge compliance are assumed to be step functions of extension, x, with a finite number of discontinuities. This assumption enables integration of the kinetic equation and its moments with respect to x analytically resulting in equations where x has been eliminated. When the constants in the rate parameters and the force function are chosen such that Hill's force-velocity relation and features of the transient kinetic and tension data can be fitted, the resulting cross-bridge mechanism is quite similar to the one proposd by Podolsky and co-workers. Because the derived constitutive equations simplify mathematical analysis, they enable the evaluation of the influences of various cross-bridge parameters on the mechanical behavior of muscle fibers. For example, (ix) Instantaneous elastic response (To - T1) and the magnitude of rapid recovery (T2 - T1) after a step length change can be explained well when the rate of attachment is assumed high for positive x. In that case T2 corresponds to the force generated by cross-bridges in the region of negative x; (ii) Kinetic transients occur as a result of the jumps that exist in the distribution of attached cross-bridges during the isometric state. Because of the hyperbolic nature of the kinetic equation, these jumps propagate in the -x direction causing rapid changes in the speed of contraction. This study is further extended to take into account of multiple action sites and cross-bridge interaction. In the simplest case (transient response after a step length change) the model reduces to set of 14 ordinary differential equations.